These equations do not admit a solution preserving 9D Poincaré
invariance.
However, in [1]} a solution was found that preserved 8D Poincaré invariance featuring a single non-trivial longitudinal direction \(y\) .
The general ansatz for the metric was
\(\begin{split} ds^2=e^{2{\cal A}(r,y)} ds_8^2 + e^{2{\cal B}(r,y)}( dr^2 +dy^2), \end{split}\) 
